There are six people at a bus stop. Each person is half the age of the next person in line. The mean age of the group is 21. How old is the youngest person?

The youngest person is 2 years old

Step-by-step explanation:

There are six people at a bus stop.

We are told that:

The mean age of the group is 21.

The total number of people is 6 people

Hence:

The total sum of their ages is 21 × 6

= 126

Each person is half the age of the next person in line.

Let the age of the first person be = x

The age of the second person = x/2

The age of the third person = x/2 ÷ 2 = x/2 × 1/2 = x/4

The age of the fourth person = x/4 ÷ 2

x/4 × 1/2 = x/8

The age of the fifth person = x/8 ÷ 2

x/8 × 1/2 = x/16

The age of the sixth person = x/16 ÷ 2

x/16 × 1/2 = x/32

Hence:

x + x/ 2 + x/4 + x/8 + x/16 + x/32 = 126

Lowest Common Denominator is 32

32x + 16x + 8x + 4x + 2x + x/32 = 126

63x /32 = 126

Cross Multiply

63x = 126 × 32

63x = 4032

x = 4032 /63

x = 64 years

Hence, the age of the first person is 64 years.

The age of the youngest person which is the sixth person is :

x/32

= 64/32

= 2 years

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204